THE BOOK--Playing The Percentages In Baseball

Here’s an idea to test the shape of the true-talent distribution:
Use real multi-season NFL data to find Pythagorean projections (raw or third order or whatever) based on yards for and yards against.  Use the distribution of (nth-order) projections as your true-talent distribution.  Test this historical distribution against a variety of functional forms to find one that fits.

Functional forms that would make sense off the top of my head:
1)Phase space (i.e. binomial distribution with true-talent-1-win 16 times as likely as true-talent-0-wins).
2)Gaussian.
3)Bifurcated Gaussian (different standard deviations on right and left).
4)Phase space times bifurcated Gaussian.
5)Falling exponential times phase space.

Too complicated for me.  I don’t know what a Bifurcated Gaussian even is, much less how to multiply it by a phase space. 

But if someone wants to do the work and send me the resulting distribution, I’ll try to make it happen.

Phil,
I’ll work something up on the distributions and send it to you.  Would .xls be acceptable?

Jeremy: I assume you’ll be sending me a table of the CDF or PDF of the talent distribution?  Then, sure, Excel is fine!  Thanks!